arXiv subjects

Jiahua Tian

Publications and source records attributed to Jiahua Tian.

At least 19 recordsLinked to original sources

arXiv2026

Galois conjugation, droplet growth, and the differential transcendence of the Ising model in nonzero field

The square-lattice Ising model is exactly solvable in zero magnetic field, but the scope of exact solutions at nonzero field remains unresolved. We show that, at every fixed dimensionless field $H=h/(k_BT)\ne 0$, its free energy and magnetization obey no algebraic differential equation in the coupling $K=J/(k_BT)$. This excludes Onsager-type formulas and broad classes of special-function expressions. Previous work left open a countable set of fields with algebraic-integer fugacities. We eliminate these exceptions using Galois conjugation and the large-order growth of droplets of reversed spins. At conjugate fugacities outside the unit circle, nearly square droplets produce coefficient growth incompatible with an algebraic differential equation. We prove that cancellations cannot remove this growth in the full pressure series. The free-energy result also holds for the Lieb lattice and square lattices with equal-length chain decorations and uniform coupling and field. In every dimension $d\ge2$, we additionally resolve fields for which $e^{-2|H|}$ has a real algebraic conjugate greater than one.

cond-mat.stat-mech↗

arXiv2026

A note on the quantization of M2-branes on local Calabi-Yau manifolds

In this note we present a detailed computation of the BPS states from M2-branes wrapping 2-cycles in local Calabi-Yau manifolds, at the level of brane quantization. For the cases of local Calabi-Yau threefolds, the supersymmetric quantum mechanics is the 1d $\mathcal{N}=4$ non-linear sigma model. We achieve systematic, physical interpretations of refined Gopakumar-Vafa (GV) invariants, first for the curve classes with fixed geometric genus, and then for curves whose geometric genus jumps. The BPS states of 5d $\mathcal{N}=1$ superconformal field theories are interpreted from the local geometries, which are presented in a number of case studies. In particular, we compute the refined GV invariants for generalized conifolds, local CY3 giving 5d $\mathcal{N}=1$ gauge theories and a singularity whose crepant resolution contains a singular divisor. For the cases of local Calabi-Yau fourfolds, we point out the supersymmetric quantum mechanics is of type $\mathcal{N}=2B$. We set up the framework for studying M2-branes wrapping 2-cycles, and discuss a few cases of M2-brane wrapping genus-0 curves with this new approach.

hep-th↗

arXiv2026

Large-Level Limit of Doubled Chern-Simons Theory Part I: Regular Sector, Boundaries and Interfaces

We study three-dimensional $BF$ theory as the large-level limit of the doubled Chern-Simons theory $G_k\times G_{-k}$ for simply connected, compact, simple $G$, a limit that connects the symmetry topological field theories of finite and continuous symmetries. Lines whose two highest weights grow linearly with $k$ at fixed difference become $BF$ lines, with magnetic flux set by their average and electric charge equal to their difference. Representing level-$k$ torus states as normalized flux-charge wave packets, we prove that every fixed modular transformation of any fixed normalizable state with regular flux converges in the strong-$*$ topology to its $BF$ counterpart. The Dehn twist gives each line exactly its Aharonov-Bohm phase at every level, while $S$ converges to a Fourier transform exchanging flux and charge, without escaping to singular holonomies or large charges. States that approach singular fluxes at large $k$ are not covered. The natural boundary 2d theory is speculated to be a decompactified boson in the abelian case $G=U(1)$, and $\dim G$ non-compact free scalars for general $G$. For $SU(2)$, we discuss the gapped interfaces between adjacent levels, which must shift some flux or charge by a finite amount. In the $k\rightarrow\infty$ limit the interface is conjectured to be the $c=1$ Runkel-Watts theory.

hep-th↗

arXiv2026

Droplets obstruct Onsager-type solutions of the Ising model in a magnetic field

Onsager solved the two-dimensional Ising model in zero field, but no solution is known in a magnetic field. We prove that in any dimension $d\ge2$, at every fixed dimensionless field outside a countable set, the free energy obeys no algebraic differential equation in the coupling, even locally. The obstruction arises from droplet geometry: the maximal droplet volume grows as the $d/(d-1)$ power of its boundary size, while an integer band in the pressure coefficients protects the extremal contributions against cancellation. Our result excludes Onsager-type solutions and closed forms in elliptic, hypergeometric, or Painlevé functions of the coupling at these fields.

cond-mat.stat-mech↗

arXiv2026

Lifts of symmetries to minimal nondegenerate extensions are unique up to fermion attachment

Gauging fermion parity in a $(2+1)$-dimensional fermionic topological order requires lifting its symmetries to the resulting bosonic theory. We give a direct tensor-categorical proof that, for a slightly degenerate braided fusion category $\mathcal{C}$ and a fixed minimal nondegenerate extension ${\cal E}$, the restriction homomorphism $r\colon\operatorname{Aut}_{\mathrm{LR}}(\mathcal{E})\to \operatorname{Aut}_{\mathrm{LR}}(\mathcal{C})$ on classes of complex-linear locality-respecting (LR) braided autoequivalences is surjective with central kernel $\mathbb{Z}/2$, generated by fermion attachment. Thus each symmetry class has exactly two LR lift classes, related by attaching the fermion to every vortex. We apply graded Morita theory to reduce the kernel to two module types on the vortex sector, corresponding to tensoring with the vacuum or the fermion. We then prove relative rigidity to show that each type determines a unique LR class, which are distinguished by fermionic self-braiding even when their actions on simple-object labels coincide. We prove surjectivity by extending graph algebras in $\mathcal{C}^{\mathrm{rev}}\boxtimes\mathcal{C}$ to Lagrangian algebras in $\mathcal{E}^{\mathrm{rev}}\boxtimes\mathcal{E}$. Our results require neither unitarity nor a ribbon structure. We illustrate the lifting ambiguity in the Laughlin state, the $SO(3)_3$ theory and the Ising topological order.

math.QA↗

arXiv2026

Inequivalent modular tensor categories with identical $S$, $T$ and $W$

It remains an open question whether the modular data $(S,T)$ together with the Whitehead-link matrix $W$ determine a modular tensor category up to ribbon equivalence. We answer negatively by constructing two braided-inequivalent Dijkgraaf--Witten modular categories for $(\mathbb Z/p\mathbb Z)^3$ for prime $p\ge5$ with identical $(S,T,W)$ and, more generally, identical Reshetikhin--Turaev invariants of all framed oriented links with at most two components under a single bijection of simple objects. The construction varies an alternating $3$-cocycle while fixing a quadratic cohomology class, using restriction to subgroups of rank at most two to match link invariants and the quadratic and alternating classes together to obstruct braided equivalence. A complete classification of modular tensor categories up to ribbon equivalence therefore requires invariants beyond those of colored framed links with at most two components. We also analytically evaluate an uncolored partition function on a closed oriented three-manifold that separates all $(p-1)/2$ equivalence classes in the family.

math.QA↗

arXiv2026

Pseudo-Gauge Stabilizers and Fibration Structure of the Cooper--Frye Map at Freeze-Out

We study the pseudo-gauge transformation (PGT) freedom at freeze-out in relativistic spin hydrodynamics. The Cooper--Frye map is shown to factor through the quotient of freeze-out data by a universal stabilizer, yielding a stratified fibration over the space of thermodynamic Lagrange multipliers. This classifies observables into base and fiber types, bounds the number of independent PGT-sensitive observables by the family-restricted fiber dimension, and implies cross-observable consistency relations. Applied to heavy-ion polarization data, the fibration structure provides a structural interpretation of the tension between $Λ$ polarization and $ϕ$-meson spin alignment as evidence that the vorticity-dominated response sector may need to be enlarged with local field-correlation data. We show that Weyl-anomaly-induced currents studied recently are classified as base observables and recover the known Belinfante--canonical obstruction $Ω_{ab}\neq\varpi_{ab}$ from the stabilizer condition.

hep-th↗

arXiv2026

Hilbert Space and Defect Hilbert Spaces Associated with Categorical Symmetries

We present a quantum mechanical approach to understanding the Hilbert space and the defect Hilbert spaces associated with line operators of BF theory combined with level-$k$ Chern-Simons theory. The defect Hilbert spaces are closely related to the category of $*$-representations of the $C^*$-algebra of the compactly supported sections of the Fell line bundle over the conjugation action groupoid $G//_{\mathrm Ad} G$, and the structure of this category and the groupoid action on the objects of this category is interpreted quantum mechanically. We show that the action of the line operators on the Hilbert space of the $BF+kCS$ TQFT is given concretely by a convolution between the kernels that represent the line operators, and that the codimension-$2$ twist and the codimension-$1$ prequantum line bundle arise as two transgressions of the same universal level $k\in H^4(BG,\mathbb{Z})$. For finite gauge group, the resulting convolution-eigenvalue formula is identified with the Verlinde formula for the (twisted) Drinfeld double $D^ω(G)$ via an explicit phase-by-phase match with the known finite modular data. For compact Lie group, the convolution-kernel eigenvalues coincide in the regular sector with the semiclassical Hopf-link $S$-kernel, identifying two complementary derivations of the same modular data.

hep-th↗

arXiv2026

Candidate Gaugings of Categorical Continuous Symmetry

Different gaugings of the global symmetry of a quantum field theory are closely related to its various phases. In this work, we study candidate gaugeable symmetries by analyzing candidate Lagrangian algebra data in the Drinfeld center of a symmetry category $\mathscr{C}^k(G)$ associated to a QFT with continuous global $G$-symmetry and possible 't Hooft anomaly labeled by an integer $k$. We use the combination of the $BF$ theory and the level-$k$ Chern-Simons theory with gauge group $G$ as a semiclassical kernel-theoretic model for the corresponding SymTFT. Under two explicit assumptions, namely that this $BF{+}k$CS theory provides the relevant SymTFT model and that the common $+1$ eigenspaces of the resulting modular kernels detect candidate Lagrangian algebra data in the continuous setting, we derive candidate modular $S$- and $T$-kernels from Hopf-link and framing correlators in $S^3$ semi-classically. We then use these kernels to obtain candidate modular invariants and candidate gaugings. The resulting formulas recover the established cases and suggest a possible extension of this kernel-theoretic picture to compact Lie groups.

hep-th↗

arXiv2026

Categorical Symmetries via Operator Algebras

We propose that the symmetry category associated to a 2D quantum field theory with 0-form $G$-symmetry with 't Hooft anomaly $k\in H^4(BG,\mathbb{Z})$ for a large class of Lie groups $G$ is the category of twisted measurable fields of Hilbert spaces over $G$ denoted by $\mathrm{Hilb}^k(G)$, which is equivalent to the category of unitary representations of $C_0(G)$ with convolution product twisted by a multiplicative bundle gerbe labeled by $k$ denoted by $\textbf{Rep}^k(C_0(G))$. We find that the Drinfeld center of the symmetry category $\mathcal{Z}(\mathrm{Hilb}^{k}(G))$ equivalent to the category of unitary representations of the groupoid $C^*$-algebra of the Fell line bundle $Σ_k$ over the conjugation action groupoid $G//_{\rm Ad} G$, denoted by $\textbf{Rep}(C^*(G//_{\rm Ad}G,Σ_k))$, where the twist is characterized by the transgression $τ(k)\in H^2(G//_{\rm Ad}G,U(1))$. To the full generality, our framework applies to a Lie group $G$ that is a direct product of a compact connected Lie group and a number of $\mathbb{R}$ or $GL(1,\mathbb{C})$ factors. We compute the braiding of anyon lines in the bulk 3D SymTFT from this formalism. Finally we provide physical examples for abelian and non-abelian $G$, and discuss the physical consequences of flat gauging continuous global symmetries.

hep-th↗

arXiv2025

Anomaly of Continuous Symmetries from Topological Defect Network

We show that the 't Hooft anomaly of a quantum field theory with continuous flavor symmetry can be detected from rearrangements of the topological defect webs implementing the global symmetry in general spacetime dimension, which is concretized in 2D by the F-moves of the defect lines. Via dualizing the defects to flat background gauge field configurations, we characterize the 't Hooft anomaly by various cohomological data of the symmetry group, where the cohomology of Lie groups with discrete topology plays the central role. We find that an extra dimension emerges naturally as a consequence of the mathematical description of the 't Hooft anomaly in the case of flat gauging.

hep-th↗

arXiv2025

Conformal Fields from Neural Networks

We use the embedding formalism to construct conformal fields in $D$ dimensions, by restricting Lorentz-invariant ensembles of homogeneous neural networks in $(D+2)$ dimensions to the projective null cone. Conformal correlators may be computed using the parameter space description of the neural network. Exact four-point correlators are computed in a number of examples, and we perform a 4D conformal block decomposition that elucidates the spectrum. In some examples the analysis is facilitated by recent approaches to Feynman integrals. Generalized free CFTs are constructed using the infinite-width Gaussian process limit of the neural network, enabling a realization of the free boson. The extension to deep networks constructs conformal fields at each subsequent layer, with recursion relations relating their conformal dimensions and four-point functions. Numerical approaches are discussed.

hep-th↗

arXiv2025

Categorical Continuous Symmetry

We define the symmetry category in 1+1d for continuous 0-form $G$-symmetry to be $\textbf{Sky}^τ(G)$, the category of skyscraper sheaves of finite dimensional vector spaces with finite support on the group manifold of $G$, where $τ\in H^4(BG,\mathbb{Z})$ is the anomaly. We propose that the corresponding 2+1d SymTFT is described by the Drinfeld center of $\textbf{Sky}^τ(G)$. We show explicitly the way that $τ$ twists the convolution tensor product of the objects of $\textbf{Sky}^τ(G)$. As a concrete example, we present the $S$ and $T$-matrices for the simple anyons of the resulting $Z(\textbf{Sky}^τ(G))$ category for $G = U(1)$, both for the cases without or with anomaly and discuss the topological boundary conditions as Lagrangian algebra of $Z(\textbf{Sky}^τ(U(1)))$. We also present the definition of $\textbf{Sky}^τ(G)$ and $Z(\textbf{Sky}^τ(G))$ for the non-abelian case of $G=SU(2)$, as well as the speculated modular data. We point out that in order to have a physically relevant center and Lagrangian algebras it is necessary to generalize $\textbf{Sky}^τ(G)$ to a larger category, which we argue to be closely related to the category of quasi-coherent sheaves on $G_\mathbb{C}$ with convolution tensor product twisted by $τ$.

hep-th↗

arXiv2025

Symmetry, Symmetry Topological Field Theory and von Neumann Algebra

We study the additivity and Haag duality of the von Neumann algebra of a quantum field theory $\mathcal{T}_\mathcal{F}$ with 0-form (and the dual $(d-2)$-form) (non)-invertible global symmetry $\mathcal{F}$. We analyze the symmetric (uncharged) sector von Neumann algebra of $\mathcal{T}_\mathcal{F}$ with the inclusion of bi-local and bi-twist operators in it. We establish the connection between the existence of these non-local operators in $\mathcal{T}_\mathcal{F}$ and certain properties of the Lagrangian algebra $\mathcal{L}$ of the extended operators in the corresponding symmetry topological field theory (SymTFT). We prove that additivity or Haag duality of the symmetric sector von Neumann algebra is violated when $\mathcal{L}$ satisfies specific criteria, thus generalizing the result of Shao, Sorce and Srivastava to arbitrary dimensions. We further demonstrate the SymTFT construction via concrete examples in two dimensions.

hep-th↗

arXiv2025

Higher Form and Higher Group Symmetries via Mirror Symmetry

In this work we uncover a connection that relates the 1-form and the 2-group symmetries of 5D SCFTs derived from geometric engineering methods to monodromies of the corresponding B-models via mirror symmetry. Viewing defects as branes wrapping relative cycles in a non-compact CY3, we find that the defect groups can be read off from the VEVs of the corresponding line operators at the leading order. Via mirror map, we find that both the 1-form and the 2-group symmetries of the SCFT are related to the monodromy at the large radius point in the B-model. Additionally, we recursively obtain closed-form expressions of instanton expansions of the VEV of Wilson lines of certain 5D theories among which some have not been obtained so far using localization methods. We further conjecture that the 2-group symmetry is given by the Mordell-Weil torsion of the universal special geometry associated to the theory, generalizing the conjecture for rank-1 theories.

hep-th↗

arXiv2025

Symmetry Topological Field Theory for Flavor Symmetry

In this Letter, we demonstrate that the Symmetry Topological Field Theory (SymTFT) associated to a Quantum Field Theory (QFT) with continuous non-abelian $G$-flavor symmetry is a $BF$-theory with gauge group $G$. We show that gauging $G$-symmetry with a flat connection yields a theory with global symmetry characterized by exchanging the conjugate variables in the quantization of $BF$-theory. We construct the extended operators that generate the $G$-flavor symmetry and the $(d-2)$-form $\text{Rep}(G)$-symmetry of the gauged QFT. We demonstrate that $BF$-theory arises as the theory characterizing $G$-flavor symmetry of a QFT in the AdS/CFT setup. 't Hooft anomalies of the $G$-flavor symmetry are realized as extra terms in the action.

hep-th↗

arXiv2025

A Tale of Bulk and Branes: Symmetry TFT of 6D SCFTs from IIB/F-theory

We study the 7D Symmetry Topological Field Theory (SymTFT) associated to a 6D SCFT from the IIB/F-theory geometric engineering approach. The 6D (2,0) or (1,0) SCFT is constructed from IIB on a non-compact complex surface possibly with 7-branes. We derive the general form of 7D SymTFT actions from the compactification of IIB action on the boundary link of the base manifold of an elliptic Calabi-Yau threefold, for both the cases with or without flavor 7-branes intersecting the boundary link. Along the way we found new terms in the SymTFT action from the worldvolume action of flavor 7-branes involving the flavor center symmetries. We crosscheck the results against those obtained from either holographic constructions or the dual M-theory picture. Our construction potentially leads to a classification of the 7D SymTFTs which parallels the known geometric classification of the 6D SCFTs.

hep-th↗

arXiv2024

3d $N=2$ theories from M-theory on CY4 and IIB brane box

We study 3D $N=2$ supersymmetric field theories geometrically engineered from M-theory on non-compact Calabi-Yau fourfolds (CY4). We establish a detailed dictionary between the geometry and topology of non-compact CY4 and the physics of 3D $N=2$ theories in three different regimes. The first one is the Coulomb branch description when the CY4 is smooth. The second one is non-abelian gauge theory when the CY4 has a degenerate $\mathbb{P}^1$-fibration structure. The third one is the strongly coupled SCFT from a CY4 singularity. We find interesting flavor symmetry enhancements in the singular limit of CY4, as well as an interesting and previously unexplored phenomenon in 3D, termed ``flavor symmetry duality''. Many examples are analyzed with an emphasis on toric CY4s and $\mathbb{C}^4$ orbifolds with crepant resolutions. We develop a new brane box method to study the physics of Coulomb branch of 3D $N=2$ theory that admits a toric construction. Via IIB/M-theory duality we find that the brane box diagram living in $\mathbb{R}^3$ can be physically realized as a configuration of intersecting 4-branes which are extended objects in 8D maximal supersymmetric theory, which is shown to be consistent via various chains of dualities. The rank, effective gauge coupling and certain hints to flavor symmetry enhancement of the 3D $N=2$ theory are read off from the brane box and cross-checked against the results obtained from geometric engineering. The exotic branes in 8D maximal supersymmetric theory and the 4-string junctions thereof are shown to play a crucial role in the construction of the brane box.

hep-th↗